Research Article Hybrid Structures Applied to Subalgebras of BCH-Algebras G. Muhiuddin , 1 D. Al-Kadi , 2 W.A. Khan, 3 and C. Jana 4 1 Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia 2 Department of Mathematics and Statistic, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia 3 Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia 4 Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India Correspondence should be addressed to G. Muhiuddin; chishtygm@gmail.com Received 17 April 2021; Accepted 4 July 2021; Published 16 July 2021 Academic Editor: Kifayat Ullah Copyright©2021G.Muhiuddinetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e algebraic structures have many applications in coding theory, cryptography, and security networks. In this paper, the notion of hybrid subalgebras of BCH-algebras is introduced and related properties are investigated. Moreover, some characterizations of hybrid subalgebras of BCH-algebras are given. Furthermore, we state and prove some theorems in hybrid subalgebras of BCH-algebras. e homomorphic images and inverse images of fuzzy BCH-subalgebras are studied and discussed. 1. Introduction e notions of BCK/BCI-algebras were initiated by Imai and Is´ eki in 1966. A number of research papers have been produced on the theory of BCK/BCI-algebras. Hu and Li [1, 2] introduced the notion of a BCH-algebra as a gen- eralization of BCK/BCI-algebras and subsequently gave examples of proper BCH-algebras and studied some properties. Certain other properties of BCH-algebras have been studied by Ahmad [3], Dudek and omys [4], Chaudhry [5], Roh et al. [6, 7], Chaudhry et al. [8], and Dar et al. [9], and Smarandache structure has been applied to BCH-algebra [10]. Fuzzy sets, which were introduced in the 1960s by Zadeh [11], have been developed considerably by many research studies. Molodtsov introduced the concept of soft set [12] and pointed out several directions for its applications (for more details, see [12–15]). is concept was applied to BCH- algebras introducing soft BCH-algebras which were studied in [16]. Moreover, the fuzzy set theoretical approach to BCH-algebras was extensively investigated by many re- searchers on different aspects. For example, fuzzy n-fold ideals [17], fuzzy closed ideals and fuzzy filters [18], filters based on bipolar-valued fuzzy sets [19], and cubic sub- algebras [20]. Jun et al. [21] combined the concepts of fuzzy sets and soft sets, introduced the notion of hybrid structure in a set of parameters over an initial universe set, and investigated several properties. ey also introduced the concepts of hybrid linear space, hybrid subalgebra, and hybrid field. Moreover, hybrid structure applications have been studied in semigroups (see [22–25] and references there in), and recently, hybrid ideals of BCK � BCI-algebras were studied in [26–29]. For more important terminologies, the readers are referred to [30–36]. In the present paper, we present an application of fuzzy set theory to an algebraic structure called, BCH-algebra. As we know it algebraic structures play a prominent role in mathematics with wide ranging applications in many disciplines such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, topological spaces, and the like. is provides sufficient motivation to researchers to review various concepts and results from the realm of abstract algebra in the broader framework of fuzzy setting. e objective of this study is to introduce the concept of hybrid subalgebras of BCH- Hindawi Security and Communication Networks Volume 2021, Article ID 8960437, 8 pages https://doi.org/10.1155/2021/8960437